Laboratory experiments are described in which a cylindrical obstacle is moved azimuthally through a rotating cylindrical tank of fluid in which a basic azimuthal flow inversely dependent upon the tank radius is generated by means of a source-sink arrangement. A technique is described whereby the flow can be adjusted until, relative to the obstacle, it is forward near the centre of the tank and reversed near the rim, with a monotonic variation between these extremes. The sense of this shear, relative to the obstacle, can be altered so that it either opposes or coincides with the sense of the basic rotation. Both cases are investigated in the experiments. The results of both qualitative and quantitative measurements are presented, and some comparison with related theoretical work is attempted.